Problem: Simplify the following expression: $z = \dfrac{-9y^2 + 99y - 162}{y - 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ z =\dfrac{-9(y^2 - 11y + 18)}{y - 2} $ Then we factor the remaining polynomial: $y^2 {-11}y + {18} $ ${-2} {-9} = {-11}$ ${-2} \times {-9} = {18}$ $ (y {-2}) (y {-9}) $ This gives us a factored expression: $\dfrac{-9(y {-2}) (y {-9})}{y - 2}$ We can divide the numerator and denominator by $(y + 2)$ on condition that $y \neq 2$ Therefore $z = -9(y - 9); y \neq 2$